Crack in a solid under Coulomb friction law. (English) Zbl 1058.74064

Kovtunenko, Victor A.

Appl. Math., Praha 45, No. 4, 265-290 (2000).

The existence of solutions to the static problem for an elastic body possessing a crack and clamped at its boundary is proved. On the crack faces the non-penetrability of mass is respected and the Coulomb friction is considered. The auxiliary problem with given friction force is employed. The feedback between the given and the resulting friction force is searched by means of the Tikhonov (“second Schauder”) fixed point theorem. This technique requires to have the crack faces sufficiently smooth (a certain partial regularity of the solution to the auxiliary problem is needed) and the coefficient of friction small enough.

Reviewer: Jiří Jarušek (Praha)

MSC:

74M15	Contact in solid mechanics
35Q72	Other PDE from mechanics (MSC2000)
74M10	Friction in solid mechanics

Keywords:

variational and quasi-variational inequalities; crack; Coulomb friction

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